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Thread: Wire cut into 3 pieces question

  1. #1
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    Question Wire cut into 3 pieces question

    A twenty-foot piece of wire is cut into three pieces. The first piece is twice as long as the second piece, and four times as long as the third piece. How long is the second piece of wire?

    Answer in the book
    The equation 2x+x+1/2x=20 modes this situation. Therefore, 3 1/2x=20, x= 5 5/7 feet

    I understand how they got 2x+x, but don't understand how they got 1/2x. Can someone explain it?

    Thanks in advance.
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  2. #2
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    Re: Wire cut into 3 pieces question

    second piece has length $x$

    first piece is twice as long as the second, so it has length $2x$

    first piece is four times as long as the third $\implies$ the third piece is $\dfrac{1}{4}$ the length of the first piece ...

    $\dfrac{1}{4} \cdot 2x = \dfrac{x}{2}$

    $2x+x+\dfrac{x}{2}=20$

    $4x+2x+x=40$

    $7x=40 \implies x= \dfrac{40}{7}=5\frac{5}{7} \, ft$

    recap ...

    second piece has length $\dfrac{40}{7}$

    first piece has length $\dfrac{80}{7}$

    third piece has length $\dfrac{20}{7}$

    Sum of those three is $\dfrac{140}{7}=20$
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